Details

analyze62.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.2s (22.6%)

Results

871.0ms	8254×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify265.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1222×	`fma-neg_binary64`
983×	`fma-def_binary64`
688×	`div-sub_binary64`
423×	`sub-neg_binary64`
412×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	35	13
3	74	13
4	151	13
5	245	13
6	641	13
7	1125	13
8	2158	13
9	2729	13
10	3037	13
11	2995	13
12	3049	13
13	3063	13
14	3569	13
15	3559	13
16	3559	13
17	3559	13
18	3559	13
19	3559	13
20	3655	13
21	3703	13
22	3785	13
23	3593	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (+.f64 x y))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series22.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
3.0ms	(-.f64 2 (+.f64 x y))

rewrite187.0ms (3.6%)

Algorithm

2×	batch-egg-rewrite

Rules

843×	`prod-diff_binary64`
283×	`egg-rr`
189×	`log1p-udef_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Counts

2 → 283

Calls

2 calls:

173.0ms	(-.f64 2 (+.f64 x y))
173.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	197	20
2	2938	20
3	4979	20
0	0	0
1	0	0

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-def_binary64`
491×	`times-frac_binary64`
379×	`associate-/l*_binary64`
373×	`fma-neg_binary64`
349×	`associate-/r*_binary64`

Counts

331 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	1184
1	421	1176
2	1580	1064
3	4994	1064
4	5237	1064

prune388.0ms (7.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	316	3	319
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	316	4	320

Error

Counts

320 → 4

Alt Table

Status	Error	Program
	30.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
	39.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
▶	13.8b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Compiler

Compiled 16260 to 9105 computations (44% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 2 (+.f64 x y))
	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	0.0b	(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
✓	2.8b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

series39.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
13.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

rewrite141.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

843×	`prod-diff_binary64`
276×	`egg-rr`
203×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
108×	`log1p-expm1-u_binary64`

Counts

2 → 276

Calls

2 calls:

129.0ms	(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
129.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	213	28
2	3109	28
3	5173	28
0	0	0
1	0	0

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Rules

466×	`cancel-sign-sub-inv_binary64`
353×	`sub-neg_binary64`
272×	`times-frac_binary64`
223×	`fma-def_binary64`
206×	`+-commutative_binary64`

Counts

324 → 334

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	2786
1	955	2762
2	3992	2726
3	5295	2726

prune834.0ms (16.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	653	0	653
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	653	4	657

Error

Counts

657 → 4

Alt Table

Status	Error	Program
▶	30.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
	39.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	13.8b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Compiler

Compiled 34765 to 20035 computations (42.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 2 (+.f64 x y))
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	0.1b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)

series101.0ms (2%)

Counts

2 → 48

Calls

2 calls:

51.0ms	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
50.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)

rewrite148.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

843×	`prod-diff_binary64`
286×	`egg-rr`
202×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Counts

2 → 286

Calls

2 calls:

135.0ms	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
135.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	223	28
2	3163	28
3	5202	28
0	0	0
1	0	0

simplify124.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-/r*_binary64`
425×	`fma-def_binary64`
393×	`times-frac_binary64`
248×	`associate-r_binary64`
237×	`associate-/l*_binary64`

Counts

334 → 345

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	3931
1	1469	3819
2	4991	3819
3	5108	3819

prune844.0ms (16.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	664	0	664
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	664	4	668

Error

Counts

668 → 4

Alt Table

Status	Error	Program
✓	30.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
▶	39.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	13.8b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Compiler

Compiled 37008 to 21848 computations (41% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

series15.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

rewrite108.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

694×	`prod-diff_binary64`
561×	`fma-udef_binary64`
321×	`fma-def_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`

Counts

1 → 57

Calls

1 calls:

106.0ms

(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	216	14
2	2628	14
3	4826	14
4	4881	14
5	4891	14
0	0	0
1	0	0

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
639×	`fma-def_binary64`
281×	`cancel-sign-sub-inv_binary64`
106×	`distribute-rgt-in_binary64`
84×	`distribute-lft-in_binary64`

Counts

81 → 65

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	321
1	42	229
2	79	229
3	108	229
4	184	229
5	306	229
6	582	229
7	876	229
8	984	229
9	1072	229
10	1065	229
11	992	229

prune49.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	65	4	69

Error

Counts

69 → 4

Alt Table

Status	Error	Program
✓	30.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) 2)
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	39.2b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	13.8b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Compiler

Compiled 1142 to 764 computations (33.1% saved)

regimes329.0ms (6.3%)

Accuracy

Total 0.0b remaining (30.2%)

Threshold costs 0.0b (30.2%)

Counts

40 → 1

Compiler

Compiled 1756 to 1207 computations (31.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	13	13
2	24	13
3	32	13
4	36	13
5	37	13
6	37	13

end103.0ms (2%)

Compiler: Compiled 72 to 49 computations (31.9% saved)

Details

analyze62.0ms (1.2%)

sample1.2s (22.6%)

simplify265.0ms (5.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series22.0ms (0.4%)

rewrite187.0ms (3.6%)

simplify70.0ms (1.4%)

prune388.0ms (7.5%)

localize11.0ms (0.2%)

series39.0ms (0.8%)

rewrite141.0ms (2.7%)

simplify104.0ms (2%)

prune834.0ms (16.1%)

localize7.0ms (0.1%)

series101.0ms (2%)

rewrite148.0ms (2.8%)

simplify124.0ms (2.4%)

prune844.0ms (16.2%)

localize6.0ms (0.1%)

series15.0ms (0.3%)

rewrite108.0ms (2.1%)

simplify49.0ms (0.9%)

prune49.0ms (0.9%)

regimes329.0ms (6.3%)

simplify5.0ms (0.1%)

end103.0ms (2%)

Profiling